Ferromagnetic half levitation of LK-99-like synthetic samples

We successfully synthesized polycrystalline LK-99-like ceramic samples with a solid-state-sintering method. Powder X-ray diffraction shows that the main contents are $\mathrm{Pb_{10-x}Cu_x(PO_4)_6O}$ and $\mathrm{Cu_2S}$, consistent with recent reports [arXiv:2307.12037; arXiv:2308.01192]. In some small flaky fragments, we successfully observed ``half levitation'' atop a $\mathrm{Nd_2Fe_{14}B}$ magnet. Using magnetization measurements on such small pieces, as well as on a large piece which does not exhibit the half levitation, we show that the samples ubiquitously contain weak yet definitive soft ferromagnetic components. We argue that, together with the pronounced shape anisotropy of the small fragments, the soft ferromagnetism is sufficient to explain the observed half levitation in strong vertical magnetic fields. Our measurements do not indicate the presence of the Meissner effect, nor zero resistance, in our samples, leading us to believe that our samples do not exhibit superconductivity. The precise chemical composition and the physics behind the ferromagnetic component remain outstanding questions to be addressed in future research.